Methods of increasing fidelity of quantum operations

ABSTRACT

Systems and methods are provided for improving fidelity of a quantum operation on a quantum bit of interest. A controlled quantum gate operation, controlled by the quantum bit of interest, id performed on an ancillary quantum bit. An energy state of the ancillary quantum bit is measured to facilitate the improvement of the fidelity of the quantum operation.

FIELD OF THE INVENTION

The invention relates generally to quantum computers. More specifically,the invention relates to generating fundamental logical operations inquantum computers.

BACKGROUND OF THE INVENTION

A classical computer operates by processing binary bits of informationthat change state according to the laws of classical physics. Theseinformation bits can be modified by using simple logic gates such as ANDand OR gates. The binary bits are physically created by a high or a lowenergy level occurring at the output of the logic gate to representeither a logical one (e.g. high voltage) or a logical zero (e.g. lowvoltage). A classical algorithm, such as one that multiplies twointegers, can be decomposed into a long string of these simple logicgates. Like a classical computer, a quantum computer also has bits andgates. Instead of using logical ones and zeroes, a quantum bit (“qubit”)uses quantum mechanics to occupy both possibilities simultaneously. Thisability means that a quantum computer can solve a large class ofproblems with exponentially greater efficiency than that of a classicalcomputer.

SUMMARY OF THE INVENTION

In accordance with an aspect of the present invention, a method isprovided for improving fidelity of a quantum operation on a quantum bitof interest. A controlled quantum gate operation, controlled by thequantum bit of interest, is performed on an ancillary quantum bit. Anenergy state of the ancillary quantum bit is measured to facilitate theimprovement of the fidelity of the quantum operation.

In accordance with another aspect of the present invention, a method isprovided for improving fidelity of a quantum gate operation. A firstquantum gate operation is performed on a first ancillary quantum bit. Asecond quantum gate operation is performed on the first ancillaryquantum bit and a second ancillary quantum bit. An energy state of thesecond ancillary quantum bit is measured to determine an energy state ofthe first ancillary quantum bit.

In accordance with still another aspect of the present invention, amethod is provided for improving fidelity of a quantum measurementoperation. A controlled NOT (CNOT) gate operation, controlled by aquantum bit of interest, is performed on an ancillary quantum bit. Anenergy state of the ancillary quantum bit is measured to determine anenergy state of the quantum bit of interest.

In accordance with yet another aspect of the present invention, a methodis provided for improving fidelity of a quantum operation on a quantumbit of interest. A controlled quantum gate operation, controlled by thequantum bit of interest, is performed on an ancillary quantum bit toproduce an entangled state of the system formed by quantum bit ofinterest and the ancillary quantum bit. The entangled state included asuperposition of a plurality of basis states. An energy state of theancillary quantum bit is measured to eliminate at least one basis statefrom the entangled state.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, objects, and advantages of the invention will become moreapparent from the detailed description set forth below when taken inconjunction with the drawings, wherein:

FIG. 1 illustrates a basic block diagram of a quantum circuit configuredto perform a quantum gate in accordance with an aspect of the presentinvention;

FIG. 2 is an energy diagram illustrating energy states in aqubit-resonator system having some degree of coupling between the qubitand the resonator;

FIG. 3 illustrates an exemplary system that could be used to performmethodologies in accordance with an aspect of the present invention;

FIG. 4 illustrates one implementation of a schematic quantum gatediagram that employs a high fidelity gate operation to improve a lowfidelity measurement in accordance with an aspect of the invention;

FIG. 5 illustrates a first quantum circuit that can be used to improvethe fidelity of an X gate in accordance with an aspect of the presentinvention;

FIG. 6 shows a second quantum circuit that can be used to improve thefidelity of an X gate in accordance with an aspect of the presentinvention;

FIG. 7 shows a third quantum circuit that can be used to improve thefidelity of an X gate in accordance with an aspect of the presentinvention;

FIG. 8 shows a fourth quantum circuit that can be used to improve thefidelity of an X gate in accordance with an aspect of the presentinvention;

FIG. 9 illustrates another implementation of a schematic quantum gatediagram that employs a high fidelity gate operation to improve a lowfidelity measurement in accordance with an aspect of the invention; and

FIG. 10 illustrates a method for improving the fidelity of a quantumoperation in accordance with an aspect of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Digital quantum gates are a technique for performing qubit gatingoperations with arbitrarily high fidelity. FIGS. 1-3 provide anexemplary architecture for performing the various gating operations ofFIG. 4-10, but it will be appreciated that the methods of increasingfidelity in readout measurements and X gates can be employed to avariety of different quantum gate technologies and architectures.

To establish some terminology, the term “sweep” is intended to refer toan adiabatic sweeps of a qubit control parameter, in which the controlparameter is adjusted slowly relative to an energy of a splittingbetween energy states of a system. In a sweep, the qubit state tracksthe energy contour of the system as the control parameter is adjusted.The fidelity of a sweep can be made arbitrarily high by lowering thesweep rate. A “jump” takes advantage of symmetries of the qubitHamiltonian to instantaneously change the energy of the system withoutchanging the state. In a jump, the control parameter is rapidly sweptfrom one point to another in which the qubit has the same energyeigenstate but may or may not have the same eigenvalue. The fidelity ofa jump can be made arbitrarily high by increasing the sweep rate.

FIG. 1 illustrates a basic block diagram of a quantum circuit 10configured to perform a quantum gate 10 in accordance with an aspect ofthe present invention. The quantum circuit 10 includes a plurality ofqubits 12 and 14, each coupled to a fixed resonator 20. In theillustrated implementation, two qubits 12 and 14 are used, but it willbe appreciated that quantum logic gates can be implemented with one,two, or more than two qubits coupled to a given resonator. One of aplurality of classical digital controls 32 and 34 are coupled to theeach of the plurality of qubits 12 and 14. The coupling between eachqubits (e.g., 12) and its corresponding classical control (e.g., 32) isarranged so that the quantum state of qubit 12 may be changed inresponse to adjustment of a classical control parameter associated withthe digital control. The term “classical” implies that the manner ofcontrol behaves generally according to the laws of classical physics.The quantum circuit of FIG. 1 has general application in quantumcomputing, and may be implemented using any quantum circuit technologyin which the energy splitting is tunable.

For example, a physical implementation of any of the plurality of qubits12 and 14 may be a Josephson junction, a quantum dot, a SQUID(superconducting quantum interference device), a Cooper pair box, or anion trap. The implementation of the resonator 20 is likewise notrestricted to a particular technology. A resonator 20 that may beemployed in accordance with the basic principles of the invention may beany system having at least two quantum states. Examples of a resonatorthat satisfy this requirement include, but are not limited to, atransmission line, a resonant cavity, and another qubit. In addition,the coupling of a qubit to a resonator may be accomplished according tothe invention using any of various means of physical coupling. Forexample, the qubit-resonator coupling may be a mechanical coupling bymeans of an electrical conductor. Alternatively, the qubit-resonatorcoupling may include, without limitation, capacitive, inductive,magnetic, nuclear, and optical coupling, or any combination of theforegoing.

FIG. 2 is an energy diagram 30 illustrating energy states in aqubit-resonator system having some degree of coupling between the qubitand the resonator. Of particular importance is the behavior of qubit andresonator energy states as the qubit is tuned to a level that wouldcorrespond to a crossing point, labeled A in the diagram. For example,for an initial state having a qubit in an excited state and theresonator in a ground state, denoted as |1,0>, as the classical controlparameter is swept slowly from Point 1 to a point corresponding tocrossing A, the effect of the coupling dominates, and the crossing atpoint A is avoided. This results from a quantum mechanical effectwhereby two systems that are coupled together and that have the sameenergy will not cross energy lines. Thus, as the classical controlparameter sweeps to Point 2, the state of the system tracks the energyline labeled |0,1>−|1,0>. This energy line asymptotically approaches theenergy line |0,1> of the uncoupled case, which is depicted in FIG. 2 asa dashed line. At point 2, the system assumes the state |0,1>, with thequbit in the ground state and the resonator in the excited state.Provided that the sweep of the classical control parameter is adiabatic,the end result is a change of state from |1,0> to |0,1>, whereby aphoton has been taken from the qubit and transferred to the resonator.In essence, the information has been swapped.

Similarly, as shown in FIG. 2, with the system in an initial state of|0,1> at Point 1, an adiabatic sweep of the classical control parametertoward Point 2 will track the energy line labeled |0,1>+|1,0>. Again,the crossing at A is avoided, and the energy line asymptoticallyapproaches energy line |1,0> of the uncoupled case, depicted in FIG. 2as a dashed line. At Point 2, the system achieves the state |1,0>,effectively swapping information between qubit and resonator.

In the illustrated diagram, the exchange of information between qubitand resonator occurs when there is an adiabatic sweep of the classicalcontrol parameter. This means that the parameter is adjusted very slowlyrelative to all other relevant time scales. For example, the relevanttime scales may be determined according to the coupling strength oraccording to the size of the energy splitting. In other words, anadiabatic sweep is one that is sufficiently slow to allow the state ofthe system to follow the energy line in which it started, withoutallowing it to cross another energy line.

FIG. 3 illustrates an exemplary system that could be used to performmethodologies in accordance with an aspect of the present invention. Thesystem 100 includes a quantum processor 110 comprising a plurality ofresonators B1-B5, C1-C5, and D1-D5, each configured to store all or aportion of the quantum information comprising a qubit. Each of theplurality of resonators can be configured as transmission lineresonators, lumped element resonators, distributed resonators, or acombination thereof. Each of the plurality of resonators can have anassociated characteristic frequency, with a first set B1, B3, B5, C2,C4, D1, D3, and D5 of the plurality of resonators having a firstassociated frequency (e.g., 10 GHz) and a second set B2, B4, C1, C3, C5,D2, and D4 of the plurality of resonators can having a second associatedfrequency (e.g., 15 GHz).

The quantum processor 110 further comprises a plurality of qubit cellsAB1-AB5, BC1-BC5, CD1-CD5, DE1-DE5, B12-D12, B23-D23, B34-D34, B45-D45,X1-X3, and R1-R3 configured to perform logical operations on the storedquantum information. In the illustrated implementation, each of thequbit cells can be implemented as one or more of a Josephson junction, aquantum dot, a SQUID (superconducting quantum interference device), aCooper pair box, or an ion trap. Each qubit cell can be coupled to oneor more resonators, such that the resonators and the qubit cells, takencollectively, can be used to perform logical operations on a qubit.

In normal operation, all of the qubits are kept in their ground stateand quantum information in stored in some fraction of the resonators.Quantum information can be routed from one resonator to another bypicking any route through empty resonators to perform digital quantumgate operations. For example, if quantum information were stored only inthe resonators of the second and fourth column, quantum informationcould be routed from B2 to D4 by sweeping qubit B23 to transfer thestate from B2 to B3. Next, sweep BC3 to transfer to C3, sweep CD3 totransfer to D3, and finally, sweep D34 to transfer to D4. It is possibleto transfer quantum information through a resonator even if it alreadycontains another piece of quantum information. Multiple qubit digitalquantum gates can be performed by transferring quantum information intotwo qubits connected to the same resonator and using the sequences ofsweeps and jumps as described in U.S. Pat. No. 7,498,832 and anapplication titled “Quantum Processor Assembly.”

The plurality of qubit cells can include multiple types of qubit cells,each having a different structure and optimized for a differentfunction. For example, a first set of qubit cells X1-X3 can be optimizedfor performing a quantum rotation, such as a Hadamard gate or an X gateoperation, on a coupled resonator (e.g., B1-D1). To this end, each ofthe first set of qubit cells is configured to have a set of energystates that can be modeled as the state of a spin-½ particle, withassociated “spin-up” and “spin-down” states that interact differentlywith an associated classical control parameter. In one implementation,the first set of qubit cells can be constructed as a superconductingflux qubit.

The second set R1-R3 of qubit cells can be configured to be read todetermine the state of one or more qubits stored in the quantumprocessor 110. For example, the second set of qubit cells can includeappropriate support equipment for allowing a high fidelity readoperation from the qubit cells. It will be appreciated, however, thatvarious systems and methods in accordance with an aspect of the presentinvention can be used to compensate for a low fidelity read operation,and thus alternative implementations of the second set of qubits arepossible. The third set AB1-AB5, BC1-BC5, CD1-CD5, DE1-DE5, B12-D12,B23-D23, B34-D34, B45-D45 of qubit cells can be optimized for use inmultiple qubit logical gate operations. To this end, each of the thirdset of qubit cells can be implemented, for example, as a singleJosephson junction. In one implementation, the third set can each beimplemented as a superconducting phase qubit.

In accordance with an aspect of the present invention, the processor canfurther comprising a conventional computer system 120 that is configuredto tune each of the plurality of qubit cells along their respectivefrequency ranges and monitor the location of quantum information withinthe processor. The conventional computer system 120 is configured toprovide respective control signals to a plurality of classical controlmechanisms (not shown) associated with the plurality of qubit cells asto adjust their associated frequencies and corresponding energy states.In addition, the system control 120 tracks the stored location ofquantum information within the processor 110, allowing information to bequickly retrieved when it is needed for a logical gate. For example,information stored in one set of resonators can be moved to resonatorsnear one or more specialized qubit cells to allow a specific logicaloperation to be performed. In one implementation, any information in theprocessor 110 will be stored in one or more resonators, as theresonators generally have coherence time superior to that of qubitcells, and the remaining qubit cells and resonators are left in theirground states to avoid any interference with the transfer of the storeddata.

FIG. 4 illustrates one implementation of a schematic quantum gatediagram 200 that employs a high fidelity gate operation to improve a lowfidelity measurement in accordance with an aspect of the invention. Inthe schematic quantum gate diagram, a quantum bit of interest, Q, whichis the qubit to be measured, is used as a control qubit in a pluralityof high fidelity gate operations 204-208 on a corresponding set of atleast one ancillary qubit. In the illustrated implementation, the highfidelity gate operation is a controlled NOT (CNOT) operation. It will beappreciated, however, that another appropriate controlled gate operationcould be used, such as a Fredkin gate or a Toffoli gate. For thesegates, it will be appreciated that the controlled gate operation bit isalso performed on a second ancillary qubit. The result of theseoperations is an entanglement of the quantum bit of interest with the atleast one ancillary qubit, A₁ . . . A₅. In the illustratedimplementation, five ancillary qubits are used, with each qubitinitialized to the ground state, such that the quantum gate operations204-208 on the ancillary qubits create an entangled state from anoriginal, arbitrary state of the qubit α|0>+β|1>, such that:α|0

+β|1

→α|000000

+β|111111

  Eq. 1

Once the entangled state has been created, each of the five ancillaqubits is measured using a corresponding low fidelity measurement214-218. When the first low fidelity measurement 214 is performed on thefirst ancilla qubit, it will project the remaining qubits into eitherthe |00000

state (with probability |α|²) or the |11111

state (with probability |β|²). All subsequent measurements should thusyield the same result. However, since the measurement is low fidelity,it will be appreciated that, due to various errors, some measurementsmay report the wrong result.

In accordance with an aspect of the present invention, a measurement214-218 can be performed on each of the ancillary qubits and a majorityvote can be performed on to determine the correct result. Accordingly,if each measurement has a fidelity, m, the error rate is (1−m), and theerror rate, R, of the majority vote can be expressed as:

$\begin{matrix}{R = {\sum\limits_{i = \frac{n + 1}{2}}^{n}{\begin{pmatrix}n \\i\end{pmatrix}\left( {1 - m} \right)^{i}m^{n - 1}}}} & {{Eq}.\mspace{14mu} 2}\end{matrix}$

By accepting the majority result from the plurality of measurements214-218, it is possibility to provide an increasingly small error rate,down to an error rate of the high fidelity gate operation, by increasingthe number of ancillary qubits. For example, if each measurement hasonly 96% fidelity, there is a 4% chance that any given measurement willgive a wrong answer. By using a majority-voting scheme with fiveancillary qubits, the probability of an incorrect measurement of thequbit, Q, is less than 0.1%.

In the implementation illustrated in FIG. 4, all of the ancillary qubitsare initialized, and then all of the high-fidelity gate operations areperformed, and finally all of the ancillary qubits are measured. Thisallows all of the ancillary qubits to be prepared in advance and allmeasurements to be performed simultaneously, reducing the total timenecessary for the measurement. Alternatively, the methodology can beimplemented by initializing an ancillary qubit, performing the highfidelity gate operation, and measuring the ancillary qubit. Thissequence is then repeated four times. This implementation has theadvantage that it only requires one ancillary qubit which is usedrepeatedly. The result is that there exists a trade-off between time andnumber of qubits required.

The discussion above assumed not only a high fidelity CNOT gate but alsohigh fidelity state initialization. However, the methodology of FIG. 4could also be used to improve poor state initialization if a highfidelity measurement is available. For example, suppose that the stateinitialization process which is supposed to set the state to |0

includes some small error, such that the state is set to |0

+ε|1

, ignoring state normalization for the sake of simplicity. When the highfidelity gates in FIG. 4 are performed, the qubit and ancillary qubitsbecome entangled. The resulting state contains 2⁶ terms of the formε^(n)|qa₁ . . . a₅), where n=a₁+a₂+ . . . +a₃. It will be appreciatedthat the initialization technique need not produce identical states forall five qubits. The value of the error can vary from one qubit toanother, such that the expression ε^(n) can be interpreted as a productof n complex numbers each of order ε. The two terms with quantum numberzero for all five ancillary qubits are |000000

and ε⁵|100000

, and thus when the measurements are performed, the qubit state will beprojected into |0

+ε⁵|1

with probability on the order of 1−6|ε|². Thus if the outcome of allfive measurements is zero, the error in the initialization is reduced bya factor ε⁴. However, if any measurement outcome is non-zero, theprocess must be repeated.

FIG. 5 illustrates a first quantum circuit 250 that can be used toimprove the fidelity of an X gate in accordance with an aspect of thepresent invention. In the illustrated circuit, a quantum bit ofinterest, Q, is in an arbitrary state α|0

+β|1

while an ancillary qubit, A, is in the ground state. A first CNOT gateoperation 252 is then performed on the ancillary qubit, with the quantumbit of interest being used as a control, entangling the states of thetwo qubits and transitioning the system to a state α|00

+β|11

. It will be appreciated that the above assumes that the CNOT gateoperation is of sufficiently high fidelity that the likelihood of errorcan be ignored.

After the entangled state has been created, the X gate operation 254 isperformed on the quantum bit of interest, Q. If the X gate operation 254has some small probability of failure |ε|², after the X gate the systemwill be in the state α|10

+β|01

+αε|00

+βε|11

. A second CNOT gate operation 256 is performed on the ancillary qubit,with the quantum bit of interest being used as a control. The secondCNOT gate operation 256 transforms the state of the system to α|11

+β|01

+αε|00

+βε|10

. It will be appreciated that after the second CNOT gate operation 256,the ancillary qubit is in an excited state in the two statesrepresenting a successful X gate operation, and the ancillary qubit isin its ground state in the two states representing a failed X gateoperation. Accordingly, a measurement 258 of the ancillary qubit can beperformed. Measurement of the ancillary qubit will yield a ground statewith probability |ε|², and an excited state with probability 1−|ε|².Where the ancillary qubit is the excited state, it is determined thatthe X gate will have been performed perfectly, up to the fidelity of theCNOT gates 252 and 256 and the measurement 258. If the ancillary qubitis measured in the ground state, the quantum bit of interest will bereturned to its original state, and the process is repeated.

FIG. 6 shows a second quantum circuit 300 that can be used to improvethe fidelity of an X gate in accordance with an aspect of the presentinvention. In the illustrated circuit, a quantum bit of interest, Q, isin an arbitrary state α|0

+β|1

while two ancillary qubits, A₁ and A₂ are prepared in the ground state.The circuit is broken into two stages: a first stage 310, labeled step1, and a second stage 320, labeled step 2. In the first stage 310, thelow fidelity X gate operation 312 is performed on the first ancillaryqubit, A₁, transforming it to the state ε|0

+|1

, where |E|² is a probability of failure of the low fidelity gateoperation 312. A CNOT gate operation 314 is then performed on the secondancillary qubit, A₂, using the first ancillary qubit as a control. TheCNOT gate operation transforms the state of the system comprising twoancillary qubits from (ε|0

)+|1

)|0

to ε|00

+|11

. Finally, a measurement 316 of the second ancillary qubit is performed,resulting in a ground state with probability |ε|² and an excited statewith probability 1−|ε|².

If the second ancillary qubit is found to be in the ground state, the Xgate is determined to be unsuccessful and the first stage is repeated.If the second ancillary qubit is in the excited state, it is determinedthat the first ancillary qubit has been successfully prepared in theexcited state. In the second stage 320, a CNOT gate operation 322 isperformed on the quantum bit of interest, Q, using the first ancillaryqubit as the control. Since the CNOT gate operation 322 is highfidelity, and the first ancillary qubit is known to be in the excitedstate, the CNOT gate operation should invert the state of the quantumbit of interest to a new state, β|0

+α|1

. To ensure that the X gate was successful, the first ancillary qubitcan be measured as well, with a measured excited state indicating asuccessful operation and a measured ground state indicating that qubit Qis unaltered from its original state.

The quantum circuits shown in FIGS. 5 and 6 are probabilistic, such thatsome fraction of the circuit will need to be repeated multiple times toproduce the desired outcome. The average number of times the circuitwill need to be repeated can be determined as (1−|ε|²)⁻¹, which willusually be close to one. For example, if the X gate had only a fiftypercent chance of operating correctly, the average number of repetitionsis only two. Each of FIGS. 5 and 6 provide advantages, with the firstcircuit using fewer qubits, and the second circuit allowing the firststage 310 to be performed in advance and the first ancillary qubitmaintained in an excited state until needed.

FIG. 7 shows a third quantum circuit 350 that can be used to improve thefidelity of an X gate in accordance with an aspect of the presentinvention. In FIG. 7, the circuits of FIGS. 4 and 5 have been combinedas to produce a circuit capable of performing a high fidelity X gategiven a high fidelity controlled gate and low fidelity X gates andmeasurement. In the illustrated implementation, the controlled gate is aCNOT gate, but it will be appreciated that another controlled gate, suchas a Toffoli gate or a Fredkin gate, can be used. In this circuit, aquantum bit of interest, Q, is the qubit to be inverted, and a pluralityof ancillary qubits, A₁ . . . A₃, are initially prepared in the groundstate. The initial state of the system is thus (α|0

+β|1

)|000

.

A first plurality of CNOT gate operations 352-354 are performed usingthe quantum bit of interest as a control and the ancillary qubits astargets. This transitions the state of the system to α|0000

+β|1111

. The low fidelity X gate 356 is performed on the quantum bit ofinterest, transforming the system to the state α|1000

+β|0111

+αε|0000

+βε|1111

, where |ε|² is an error rate of the X gate. A second plurality of CNOTgate operations 362-364 are then performed using the quantum bit ofinterest as a control and the ancillary qubits as targets, resulting inthe state α|1111

+β|0111

+αε|0000

+βε|1000

. Measurements 366-368 are then performed on the ancillary qubits. Whenthe first measurement is performed, the system will be projected intothe state (α|1)+β|0

)|111

with probability 1−|ε|², and the state (α|0)+β|1

)|000

with probability |ε|².

If each measurement has an error rate δ, then the probability of allthree measurements 366-368 reporting correctly is (1−δ)³. Theprobability of two or more measurements reporting incorrectly is on theorder of δ². Accordingly, it is determined which value of the ancillaryqubits is obtained in the majority of the measurements, and theeffectiveness of the X gate operation is determined from the majorityvalue. If a majority of the ancillary qubits are determined to be in theexcited state, the X gate is determined to be successful. If a majorityof the ancillary qubits are determined to be in a ground state, thecircuit must be repeated. The fact that the circuit may need to berepeated multiple times makes calculation of the probability ofsuccess/failure complicated, but the probability that the circuit willfail will be on the order of √{square root over (δ^(n))}, where n is thenumber of ancillary qubits used. On average, the circuit will berepeated (1−|ε|²)⁻¹ times.

FIG. 8 illustrates a fourth quantum circuit 400 that can be used toimprove the fidelity of an X gate in accordance with an aspect of thepresent invention. In FIG. 8, the circuits of FIGS. 4 and 6 have beencombined as to produce a circuit capable of performing a high fidelity Xgate given a high fidelity controlled gate and low fidelity X gates andmeasurement. In the illustrated implementation, the controlled gate is aCNOT gate, but it will be appreciated that another controlled gate, suchas a Toffoli gate or a Fredkin gate, can be used. In this circuit, aquantum bit of interest, Q, is the qubit to be inverted, and a pluralityof ancillary qubits, A₁ . . . A₄, are initially prepared in the groundstate. The initial state of the system is thus (α|0

+β|1

)|0000

.

The circuit is broken into two stages: a first stage 410, labeled step1, and a second stage 420, labeled step 2. In the first stage 410, thelow fidelity X gate operation 412 is performed on the first ancillaryqubit, A₁, transforming it to the state ε|0

+|1

, where |ε|² is a probability of failure of the low fidelity gateoperation 412. A plurality of CNOT gate operations 414-416 are thenperformed using the first ancillary qubit, A₁, as a control and thesecond, third, and fourth ancillary qubits as targets. This transitionsthe state of the system comprising the ancillary qubits to ε|0000

+|1111

. Measurements 417-419 are then performed on the second, third, andfourth ancillary qubits. When the measurement 417 on the secondancillary qubit is performed, the system comprising the ancillary qubitswill be projected into the state |1111

with probability 1−|ε|², and the state |0000

with probability |ε|².

If each measurement has an error rate δ, then the probability of allthree measurements 417-419 reporting correctly is (1−δ)³. Theprobability of two or more measurements reporting incorrectly is on theorder of δ². Accordingly, it is determined which value of the ancillaryqubits is obtained in the majority of the measurements, and theeffectiveness of the X gate operation is determined from the majorityvalue. If a majority of the ancillary qubits are determined to be in aground state, the first stage 410 must be repeated. If a majority of theancillary qubits are determined to be in the excited state, the X gateis determined to be successful, and the first ancillary qubit isdetermined to be in an excited state, and the second stage 420 of thequantum circuit is initiated. In the second stage 420, a CNOT gateoperation 422 is performed on the quantum bit of interest, Q, using thefirst ancillary qubit as the control. Since the CNOT gate operation 422is high fidelity, and the first ancillary qubit is in the excited state,the CNOT gate operation should invert the state of the quantum bit ofinterest to a new state, β|0

+α|1

. To ensure that the X gate was successful, the first ancillary qubitcan be measured as well, with a measured excited state indicating asuccessful operation and a measured ground state indicating that qubit Qis unaltered from its original state.

FIG. 9 illustrates another implementation of a schematic quantum gatediagram that employs a high fidelity gate operation to improve a lowfidelity measurement in accordance with an aspect of the invention. Inthe schematic quantum gate diagram, a quantum bit of interest, Q, isused as a control qubit in a plurality of high fidelity gate operations452, 454, 455, 457, 458, 460 on a corresponding set of at least oneancillary qubit. In the illustrated implementation, the high fidelitygate operation is a Fredkin gate operation. Further, a plurality of Xgates 453, 456, 459 are performed on a first ancillary qubit, A₀, thatis a target of each of the Fredkin operations. A gate operations 452-460are ordered such that, when a first ancillary qubit, A₀, is prepared inthe |0

+|1

state, the combination of two Fredkin gates (e.g., 452 and 454) betweenthe first ancillary qubit, A₀, and one of the ancillary qubits to bemeasured and the X gate (e.g., 453) on first ancillary qubit, A₀,simulate a CNOT gate between the quantum bit of interest and the qubitto be measured.

The result of a set of gate operations is an entanglement of the quantumbit of interest, Q, with at one of the ancillary qubits, A₁ . . . A₃. Inthe illustrated implementation, the quantum bit of interest is entangledwith each ancillary qubit other than the first ancillary qubit. Once theentangled state has been created, each of the entangled ancilla qubitsis measured using a corresponding low fidelity measurement 464-466, amajority vote can be performed to determine the correct result. Byaccepting the majority result from the plurality of measurements464-466, it is possibility to provide an increasingly small error rate,down to an error rate of the high fidelity gate operation, by increasingthe number of ancillary qubits.

FIG. 10 illustrates a method 500 for improving the fidelity of a quantumoperation in accordance with an aspect of the present invention. At 502,a controlled quantum gate operation, controlled by the quantum bit ofinterest, is performed on at least one ancillary quantum bit. It will beappreciated that after a controlled gate operation, the respectivestates of the ancillary bits are directly dependent on the state of thebit of interest, such that the controlled quantum gate operationproduces an entangled state of the system formed by quantum bit ofinterest and the at least one ancillary quantum bit. The entangled statecomprising a superposition of a plurality of basis states.

At 504, an energy state of one or more of the at least one ancillaryquantum bit is measured to eliminate at least one basis state from theentangled state. Essentially, the wavefunction of the system formed byquantum bit of interest and the at least one ancillary quantum bit suchthat the amplitude of at least one basis state of the wavefunction isreduced to zero. By selectively ordering the quantum operation, thecontrolled quantum gate operation of 502, and the measurement of 504, itis possible to improve the fidelity of another gate operation, such asan X-gate, a measurement, or an initialization of a qubit to an excitedstate for other logical operations.

The invention has been disclosed illustratively. Accordingly, theterminology employed throughout the disclosure should be read in anexemplary rather than a limiting manner. Although minor modifications ofthe invention will occur to those well versed in the art, it shall beunderstood that what is intended to be circumscribed within the scope ofthe patent warranted hereon are all such embodiments that reasonablyfall within the scope of the advancement to the art hereby contributed,and that that scope shall not be restricted, except in light of theappended claims and their equivalents.

Having described the invention, we claim:
 1. A method for improvingfidelity of a quantum operation on a quantum bit of interest,comprising: performing respective controlled quantum gate operationsusing physical qubit assemblies and a corresponding control, eachcontrolled by the quantum bit of interest, on a plurality of ancillaryquantum bits; measuring an energy state of each of the plurality ofancillary quantum bit to facilitate the improvement of the fidelity ofthe quantum operation; and determining one of an energy state of thequantum bit of interest and an effectiveness of the quantum operationbased on the energy states of a majority of the ancillary quantum bits.2. The method of claim 1, wherein each of the controlled quantum gateoperations are controlled NOT (CNOT) gate operations.
 3. The method ofclaim 2, wherein the quantum operation is an X-gate operation, and themethod further comprising: performing the X gate operation on thequantum bit of interest after the CNOT gate operation on the ancillaryquantum bits and the quantum bit of interest; and performing respectivesecond CNOT gate operation, controlled by the quantum bit of interest onthe ancillary quantum bits prior to the measuring of the energy state ofthe ancillary quantum bit and each of the plurality of additionalancillary quantum bits.
 4. The method of claim 1, wherein at least oneof the plurality of quantum gate operations is a controlled NOT (CNOT)gate operation.
 5. The method of claim 4, further comprising: performingan X gate operation on the quantum bit of interest after the CNOT gateoperation; and performing a second CNOT gate operation, controlled bythe quantum bit of interest, on the ancillary quantum bits prior to themeasuring of the energy state of the ancillary quantum bits.
 6. Themethod of claim 1, wherein the controlled quantum gate operation is alsocontrolled by an additional quantum bit, wherein the controlled quantumgate operation is a Toffoli gate operation.
 7. The method of claim 1,wherein the controlled quantum gate operation is a Fredkin gateoperation.
 8. The method of claim 7, further comprising sequentiallyperforming an X-gate operation on the second ancillary quantum bitfollowed by one or more Fredkin gate operations on the quantum bit ofinterest, the second ancillary quantum bit and the one or moreadditional ancillary quantum bits, such that the sequentially performedX-gate operations and one or more Fredkin operations provide anequivalent operation to a plurality of CNOT operations and measuring anenergy state of each of the ancillary quantum bit and the plurality ofadditional ancillary quantum bits and determining an energy state of thequantum bit of interest based on the energy states of a majority of theancillary quantum bit and plurality of additional ancillary quantumbits.
 9. A method for improving fidelity of a quantum gate operation,comprising: performing a first controlled NOT (CNOT) gate operationusing physical qubit assemblies and a corresponding control, controlledby a quantum bit of interest, on an ancillary quantum bit; performing anX gate operation on the quantum bit of interest after the CNOT gateoperation; and performing a second CNOT gate operation on the quantumbit of interest and the ancillary quantum bit prior to the measuring ofthe energy state of the ancillary quantum bit; and measuring an energystate of the ancillary quantum bit.
 10. The method of claim 9, furthercomprising: performing a CNOT gate operation on each of a plurality ofadditional ancillary quantum bits and the quantum bit of interest;measuring an energy state of each of the plurality of additionalancillary quantum bits; and determining an energy state of the quantumbit of interest based on the energy states of a majority of theancillary quantum bit and plurality of additional ancillary physicalquantum bits.
 11. The method of claim 10, further comprising: performingthe X gate operation on the quantum bit of interest after the CNOT gateoperation on the quantum bit of interest and the ancillary quantum bitand the CNOT gate operation on each of a plurality of additionalancillary quantum bits and the quantum bit of interest; and performing asecond CNOT gate operation on the quantum bit of interest and theancillary quantum bit and the quantum bit of interest and each of theplurality of additional ancillary quantum bits after the X gateoperation and prior to the measuring of the energy state of theancillary quantum bit and each of the plurality of additional ancillaryquantum bits.
 12. A method for performing a high fidelity rotation of aquantum bit of interest, comprising: performing one of an X-gate, aY-gate, and a Z-gate operation, using a physical qubit assembly and acorresponding control, on a first ancillary quantum bit; performing acontrolled quantum gate operation on the first ancillary quantum bit anda second ancillary quantum bit; measuring the second ancillary quantumbit to determine an energy state of the second ancillary quantum bit;and performing a controlled quantum gate operation on the firstancillary quantum bit and the quantum bit of interest if the secondancillary quantum bit is in a desired energy state.
 13. The method ofclaim 12, wherein the high fidelity rotation of a quantum bit ofinterest is an X-gate and: performing one of an X-gate, a Y-gate, and aZ-gate operation on the first ancillary quantum bit comprises performingan X-gate on the first ancillary quantum bit; performing the controlledquantum gate operation on the first ancillary quantum bit and a secondancillary quantum bit comprising performing a controlled NOT (CNOT) gatecontrolled by the first quantum bit; and performing a controlled quantumgate operation on the first ancillary quantum bit and the quantum bit ofinterest if the second ancillary quantum bit is in a desired energystate comprises performing a CNOT gate controlled by the first ancillaryqubit.
 14. The method of claim 12, further comprising measuring thefirst ancillary quantum bit to ensure that the controlled gate operationresulted in the rotation to the quantum bit of interest.